A child is stationary on a swing. (a) The child is given a push by his brother to start him swinging. His brother applies a steady force of 84 N over a distance of 0.25 m. (i) Calculate the work done by this force. (ii) State how much energy is transferred by this force. (iii) After several more pushes, the child has a kinetic energy of 71 J. The mass of the child is 27 kg. Show that the velocity of the child at this point is about 2.3 m/s.

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A child is stationary on a swing - Edexcel - GCSE Physics - Question 5 - 2012 - Paper 1

Question 5

A child is stationary on a swing. (a) The child is given a push by his brother to start him swinging. His brother applies a steady force of 84 N over a distance of ... show full transcript

Worked Solution & Example Answer:A child is stationary on a swing - Edexcel - GCSE Physics - Question 5 - 2012 - Paper 1

Step 1

Calculate the work done by this force.

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Answer

To calculate the work done (W), we use the formula:

$W = F imes d$

where:

$F$ is the force applied (84 N)
$d$ is the distance over which the force is applied (0.25 m)

Substituting the values:

$W = 84 imes 0.25 = 21 ext{ J}$

Step 2

State how much energy is transferred by this force.

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Answer

The energy transferred by this force is equal to the work done, which is 21 J.

Step 3

Show that the velocity of the child at this point is about 2.3 m/s.

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Answer

To find the velocity (v) of the child, we can use the kinetic energy formula:

$KE = \frac{1}{2} mv^2$

where:

$KE$ is the kinetic energy (71 J)
$m$ is the mass of the child (27 kg)

Rearranging the formula to solve for velocity:

$v = \sqrt{\frac{2 \cdot KE}{m}}$

Substituting the values:

$v = \sqrt{\frac{2 \cdot 71}{27}} \approx 2.3 ext{ m/s}$

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